Interaction of gas fronts
Authors:
A. A. Lacey and J. L. Vázquez
Journal:
Quart. Appl. Math. 50 (1992), 469-478
MSC:
Primary 76L05; Secondary 76N15
DOI:
https://doi.org/10.1090/qam/1178428
MathSciNet review:
MR1178428
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: During rock blasting separate charges initiate movement of gas at high pressure through fractured rock. This gas occupies regions of compact support enclosed by moving boundaries, the gas fronts, at which the pressure is effectively zero. Here we consider the local behaviour of such gas fronts, albeit taking the system to be rather simpler so that the gas flow can be modelled by the porous medium equation, when two identically pressurized regions interact and when a gas front impinges upon a fixed boundary where the pressure is zero.
- G. I. Barenblatt, On self-similar solutions of the Cauchy problem for a nonlinear parabolic equation of unsteady filtration of a gas in a porous medium, Prikl. Mat. Meh. 20 (1956), 761–763 (Russian). MR 0086580
H. E. Erhie, D. Phil. thesis, Oxford University, 1988
- Juan R. Esteban and Juan L. Vázquez, Homogeneous diffusion in ${\bf R}$ with power-like nonlinear diffusivity, Arch. Rational Mech. Anal. 103 (1988), no. 1, 39–80. MR 946969, DOI https://doi.org/10.1007/BF00292920
- R. E. Grundy, A mathematical model for rock blasting involving a degenerate nonlinear diffusion equation, Quart. J. Mech. Appl. Math. 43 (1990), no. 2, 173–188. MR 1059002, DOI https://doi.org/10.1093/qjmam/43.2.173
- R. E. Pattle, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math. 12 (1959), 407–409. MR 114505, DOI https://doi.org/10.1093/qjmam/12.4.407
G. I. Barenblatt, On the self-similar solutions of the Cauchy problem for nonlinear parabolic equation of nonstationary filtration, Prikl. Math. Mech. 20, 761–763 (1956)
H. E. Erhie, D. Phil. thesis, Oxford University, 1988
J. R. Esteban and J. L. Vazquez, Homogeneous diffusion in $\mathbb {R}$ with power like nonlinear diffusivity, Arch. Rat. Mech. Anal. 103, 39–80 (1988)
R. E. Grundy, A mathematical model for rock blasting involving a degenerate nonlinear diffusion equation, Quart J. Mech. Appl. Math. 43, 173–188 (1990)
R. E. Pattle, Diffusion from an instantaneous point source with concentration dependent coefficient, Quart J. Mech. Appl. Math. 12, 407–409 (1959)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
76L05,
76N15
Retrieve articles in all journals
with MSC:
76L05,
76N15
Additional Information
Article copyright:
© Copyright 1992
American Mathematical Society